10
Physics of Masssive Neutrinos Milos 20-24/05/08 Dark Matter exists! What is the nature of dark matter? It is not known. However: It is not known. However: It possesses gravitational interactions (from the rotation curves) It possesses gravitational interactions (from the rotation curves) No other long range interaction is allowed. Otherwise it would have formed “atoms” and, hence, stars etc. So No other long range interaction is allowed. Otherwise it would have formed “atoms” and, hence, stars etc. So It is electrically neutral It is electrically neutral It does not interact strongly (if it did, it should have already been detected) It does not interact strongly (if it did, it should have already been detected) It may (hopefully!) posses some very weak interaction It may (hopefully!) posses some very weak interaction This will depend on the assumed theory  This will depend on the assumed theory  WIMPs (Weakly Interacting Massive Particles) Such an interaction may be exploited for its direct detection Such an interaction may be exploited for its direct detection The smallness of the strength of such an interaction and its low energy makes its direct detection extremely difficult. The smallness of the strength of such an interaction and its low energy makes its direct detection extremely difficult.

12
Physics of Masssive Neutrinos Milos 20-24/05/08 A: SUSY MODELS The most favorable candidate is the neutralino (a Majorana Fermion) The most favorable candidate is the neutralino (a Majorana Fermion) The rates predicted depend on the choice of the parameters in the SUSY allowed parameter space. The rates predicted depend on the choice of the parameters in the SUSY allowed parameter space. Detectable rates near the present experimental goals are predicted to be possible, but unlikely. Detectable rates near the present experimental goals are predicted to be possible, but unlikely. One may use the available limits to constrain the nucleon cross section. One may use the available limits to constrain the nucleon cross section.

14
Physics of Masssive Neutrinos Milos 20-24/05/08 B. Universal Extra Dimension Theories (e.g. Servant et al) Kaluza-Klein Theories: A tower of new particles Kaluza-Klein Theories: A tower of new particles Postulate a discreet symmetry: K-K parity Postulate a discreet symmetry: K-K parity The even modes (ordinary particles) have K-K parity +1 The even modes (ordinary particles) have K-K parity +1 The odd modes (exotic) have K-K parity -1 The odd modes (exotic) have K-K parity -1 The lightest odd mode is absolutely stable The lightest odd mode is absolutely stable The interactions of the new particles are the same with those of SM The interactions of the new particles are the same with those of SM Essentially only the particle’s mass is unknown parameter Essentially only the particle’s mass is unknown parameter

17
Physics of Masssive Neutrinos Milos 20-24/05/08 A: Conversion of the energy of the recoiling nucleus into detectable form (light, heat, ionization etc.) The WIMP is non relativistic, β≤10 -3. The WIMP is non relativistic, β≤10 -3. With few exceptions, it cannot excite the nucleus. It only scatters off elastically: With few exceptions, it cannot excite the nucleus. It only scatters off elastically: Measuring the energy of the recoiling nucleus is extremely hard: Measuring the energy of the recoiling nucleus is extremely hard: -Low event rate (much less than 10 per Kg of target per year are expected). -Low event rate (much less than 10 per Kg of target per year are expected). -Bothersome backgrounds (the signal is not very characteristic). -Bothersome backgrounds (the signal is not very characteristic). -Threshold effects. -Threshold effects. -Quenching factors. -Quenching factors.

18
Physics of Masssive Neutrinos Milos 20-24/05/08 The event rate for the coherent mode The number of events during time t is given by: The number of events during time t is given by:Where: t depends on nuclear physics, the WIMP mass and the velocity distribution t depends on nuclear physics, the WIMP mass and the velocity distribution ρ(0): the local WIMP density≈0.3 GeV/cm 3. ρ(0): the local WIMP density≈0.3 GeV/cm 3. μ r is the WIMP-Nucleus reduced mass μ r is the WIMP-Nucleus reduced mass σ S p,χ : the WIMP-nucleon cross section. It is computed in a particle model. σ S p,χ : the WIMP-nucleon cross section. It is computed in a particle model. It can be extracted from the data once f coh (A,m χ ) is known It can be extracted from the data once f coh (A,m χ ) is known

23
Physics of Masssive Neutrinos Milos 20-24/05/08 Novel approaches: Exploitation of other signatures of the reaction The modulation effect: The seasonal, due to the motion of the Earth, dependence of the rate. The modulation effect: The seasonal, due to the motion of the Earth, dependence of the rate. The excitation of the nucleus (in some cases, heavy WIMP etc, that this is realistic) and detection of the subsequently emitted de- excitation γ rays. The excitation of the nucleus (in some cases, heavy WIMP etc, that this is realistic) and detection of the subsequently emitted de- excitation γ rays. Asymmetry measurements in directional experiments (the direction of the recoiling nucleus must also be measured). Asymmetry measurements in directional experiments (the direction of the recoiling nucleus must also be measured). Detection of other particles (electrons, X-rays), produced during the LSP-nucleus collision Detection of other particles (electrons, X-rays), produced during the LSP-nucleus collision

24
Physics of Masssive Neutrinos Milos 20-24/05/08 The bothersome backgrounds Anyway it will be necessary to detect nuclear recoils Anyway it will be necessary to detect nuclear recoils At this level, processes which are ordinarily harmless can become a serious background, since they have the same signature with the good events. At this level, processes which are ordinarily harmless can become a serious background, since they have the same signature with the good events. One must see some recoil events. The background is minimized but still there. One must see some recoil events. The background is minimized but still there. One such background may come from solar neutrinos. One such background may come from solar neutrinos.

25
Physics of Masssive Neutrinos Milos 20-24/05/08 The differential elastic neutrino- nucleus cross section M V and M A are the nuclear matrix elements associated with the vector and axial current and T A is the nuclear recoil energy. M V and M A are the nuclear matrix elements associated with the vector and axial current and T A is the nuclear recoil energy.

35
Physics of Masssive Neutrinos Milos 20-24/05/08 The Quenching factor: The quenching factor for a given detector is the ratio of the signal height of a nuclear recoil event divided by the corresponding one of an electron with the same energy. The quenching factor for a given detector is the ratio of the signal height of a nuclear recoil event divided by the corresponding one of an electron with the same energy. The quenching factor must be determined experimentally for a given detector. The quenching factor must be determined experimentally for a given detector. In our calculation it was adequate to multiply the energy by an energy dependent quenching factor given by a Lidhard type theory. In our calculation it was adequate to multiply the energy by an energy dependent quenching factor given by a Lidhard type theory.

46
Physics of Masssive Neutrinos Milos 20-24/05/08 Conclusions: No experiment has directly seen any WIMP events. The expected event rate is very low. So.. The coherent WIMP event rate for a target of 1 Kg of mass in the case of a heavy WIMP increases with A. The coherent WIMP event rate for a target of 1 Kg of mass in the case of a heavy WIMP increases with A. The coherent neutrino event rate for a target of 1 Kg of mass varies as N 2 /A. The recoil energy decreases with A. The coherent neutrino event rate for a target of 1 Kg of mass varies as N 2 /A. The recoil energy decreases with A. Both rates decrease as the threshold energy increases, but the solar neutrino event rate does much more so. Both rates decrease as the threshold energy increases, but the solar neutrino event rate does much more so. Both are sensitive to quenching, but its effect on the solar neutrino event rate is much more dramatic. Both are sensitive to quenching, but its effect on the solar neutrino event rate is much more dramatic. The WIMP event rate is sensitive to the nuclear form factor, but the solar neutrino event rate is not. The WIMP event rate is sensitive to the nuclear form factor, but the solar neutrino event rate is not.

47
Physics of Masssive Neutrinos Milos 20-24/05/08 Conclusions The boron neutrinos are not a serious background to WIMP detection, unless the event rate turns out to be The boron neutrinos are not a serious background to WIMP detection, unless the event rate turns out to be less than 1 event per ton per year less than 1 event per ton per year Even below this level one can minimize the neutrino background by a judicious choice of the target and exploiting the energy cut off Even below this level one can minimize the neutrino background by a judicious choice of the target and exploiting the energy cut off

48
Physics of Masssive Neutrinos Milos 20-24/05/08 Conclusions: Directional experiments The neutrino background gives an entirely different signature compared to the WIMP signal in Directional Experiments*. In such experiments this background can be discarded at any level The neutrino background gives an entirely different signature compared to the WIMP signal in Directional Experiments*. In such experiments this background can be discarded at any level * Experiments in which the direction of the recoiling nucleus is also observed.

58
Physics of Masssive Neutrinos Milos 20-24/05/08 The directional event rate* (The direction of recoil is observed) The event rate in directional experiments is: The event rate in directional experiments is: R dir =(κ/2π)R 0 [1+h m cos(α-α m π)] R dir =(κ/2π)R 0 [1+h m cos(α-α m π)] R 0 is the average usual (non-dir) rate R 0 is the average usual (non-dir) rate α the phase of the Earth (as usual) α the phase of the Earth (as usual) α m is the shift in the phase of the Earth (it depends on μ r and the direction of observation) α m is the shift in the phase of the Earth (it depends on μ r and the direction of observation) κ/2π is the reduction factor (it depends on μ r and the direction of observation) κ/2π is the reduction factor (it depends on μ r and the direction of observation) κ and α m depend only slightly on SUSY parameters κ and α m depend only slightly on SUSY parameters * Calculations by Faessler and JDV * Calculations by Faessler and JDV

63
Physics of Masssive Neutrinos Milos 20-24/05/08 NON RECOIL MEASUREMENTS (a) Measurement of ionization electrons produced directly during the WIMP-nucleus collisions (Moustakidis, Ejiri and JDV) (a) Measurement of ionization electrons produced directly during the WIMP-nucleus collisions (Moustakidis, Ejiri and JDV) (b) Measurement of hard X-rays following the de-excitation of the atom in (a) (b) Measurement of hard X-rays following the de-excitation of the atom in (a) (Ejiri, Moustakidis and JDV) (Ejiri, Moustakidis and JDV) (c) Excitation of the Nucleus and observation of the de-excitation γ rays (c) Excitation of the Nucleus and observation of the de-excitation γ rays

72
Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS A: K-K WIMPS Theoretical advantages: Only the masses are unknown parameters. The couplings are S.M Theoretical advantages: Only the masses are unknown parameters. The couplings are S.M Experimental advantages: The WIMP energy is an order of magnitude bigger Experimental advantages: The WIMP energy is an order of magnitude bigger The energy transfer to the nucleus is a bit higher. One has a better chance to excite the nucleus The energy transfer to the nucleus is a bit higher. One has a better chance to excite the nucleus Limits K-K Nucleon cross sections can be extracted from current limits via: Limits K-K Nucleon cross sections can be extracted from current limits via: σ (K-K) (coh) ≈(A/Z) 2 10 (-6) pb [m (K-K) /200GeV] σ (K-K) (coh) ≈(A/Z) 2 10 (-6) pb [m (K-K) /200GeV] σ (K-K) (spin) ≈10 (-2) pb [m (K-K) /200GeV] σ (K-K) (spin) ≈10 (-2) pb [m (K-K) /200GeV]

73
Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS- SUSY WIMPS Standard Rates (theory) Most of the uncertainties come from the fact that the allowed SUSY parameter space has not been sufficiently sharpened. Most of the uncertainties come from the fact that the allowed SUSY parameter space has not been sufficiently sharpened. The other uncertainties (nuclear form factor, structure of the nucleon, quenching factor, energy threshold) could also affect the results by an order of magnitude. The other uncertainties (nuclear form factor, structure of the nucleon, quenching factor, energy threshold) could also affect the results by an order of magnitude. Most of the parameter space yields undetectable rates. Most of the parameter space yields undetectable rates. The coherent contribution due to the scalar interaction is the most dominant. The coherent contribution due to the scalar interaction is the most dominant.

74
Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS-Modulation (theory) The modulation amplitude h is small, less than 2% and depends on the LSP mass. The modulation amplitude h is small, less than 2% and depends on the LSP mass. It crucially depends on the velocity distribution It crucially depends on the velocity distribution Unfortunately even its sign is uncertain for intermediate and heavy nuclei. Unfortunately even its sign is uncertain for intermediate and heavy nuclei. It may increase as the energy cut off remains big (as in the DAMA experiment), but at the expense of the number of counts. The DAMA experiment maybe consistent with the other experiments, if the spin interaction dominates. It may increase as the energy cut off remains big (as in the DAMA experiment), but at the expense of the number of counts. The DAMA experiment maybe consistent with the other experiments, if the spin interaction dominates. The modulation is reduced further in the case of exotic WIMP velocity distributions The modulation is reduced further in the case of exotic WIMP velocity distributions

75
Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS -Directional Experiments The predicted rates are down by at least a factor of 4π compared to those of the standard experiments. However: The predicted rates are down by at least a factor of 4π compared to those of the standard experiments. However: Strong correlations of the event rates with the sun’s direction of motion are expected. Thus large asymmetries are expected. Strong correlations of the event rates with the sun’s direction of motion are expected. Thus large asymmetries are expected. The modulation now is much larger. The location of its maximum depends on the direction of observation. Thus it cannot be mimicked by seasonal variations of the background. The modulation now is much larger. The location of its maximum depends on the direction of observation. Thus it cannot be mimicked by seasonal variations of the background.

76
Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS: Electron production during LSP-nucleus collisions During the neutralino-nucleus collisions, electrons may be kicked off the atom During the neutralino-nucleus collisions, electrons may be kicked off the atom Electrons can be identified easier than nuclear recoils (Needed: Low threshold, ~0.25keV, TPC detectors) Electrons can be identified easier than nuclear recoils (Needed: Low threshold, ~0.25keV, TPC detectors) The branching ratio for this process depends on the threshold energies and the LSP mass. The branching ratio for this process depends on the threshold energies and the LSP mass. For a threshold energy of 0.25 keV the ionization event rate in the case of a heavy target can exceed the rate for recoils by an order of 10. For a threshold energy of 0.25 keV the ionization event rate in the case of a heavy target can exceed the rate for recoils by an order of 10. Detection of hard X-rays also seams feasible Detection of hard X-rays also seams feasible

82
Physics of Masssive Neutrinos Milos 20-24/05/08 Unfortunately, Not all available energy is exploitable! For ground to ground transitions For ground to ground transitions For Transitions to excited states For Transitions to excited states Sharply peaked at ξ=1 Sharply peaked at ξ=1

85
Physics of Masssive Neutrinos Milos 20-24/05/08 The directional event rate The event rate in directional experiments is: The event rate in directional experiments is: R dir =(κ/2π)R 0 [1+cos(α-α m π)] R dir =(κ/2π)R 0 [1+cos(α-α m π)] R 0 is the average usual (non-dir) rate R 0 is the average usual (non-dir) rate α the phase of the Earth (as usual) α the phase of the Earth (as usual) α m is the shift in the phase of the Earth (it depends on μ r and the direction of observation) α m is the shift in the phase of the Earth (it depends on μ r and the direction of observation) κ/2π is the reduction factor (it depends on μ r and the direction of observation) κ/2π is the reduction factor (it depends on μ r and the direction of observation) κ and α m depend only slightly on SUSY κ and α m depend only slightly on SUSY

100
Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS-Transitions to excited states For neutralino transitions to excited states are possible in few odd A nuclei*. For neutralino transitions to excited states are possible in few odd A nuclei*. When allowed, are kinematically suppressed When allowed, are kinematically suppressed The branching ratio depends on the structure of the nucleus and the LSP mass The branching ratio depends on the structure of the nucleus and the LSP mass In the case of Iodine, a popular target for recoils, it can be as high as 7% for LSP mass higher than 200 GeV In the case of Iodine, a popular target for recoils, it can be as high as 7% for LSP mass higher than 200 GeV * For K-K WIMPS it is quite easy * For K-K WIMPS it is quite easy

101
Physics of Masssive Neutrinos Milos 20-24/05/08 II: Cosmological Evidence for dark matter The 3 main reasons for the Big Bang Scenario: The 3 main reasons for the Big Bang Scenario: The receding of Galaxies (red shift) (Hubble 1929) The receding of Galaxies (red shift) (Hubble 1929) The Microwave Background Radiation (CMBR – Penzias and Wilson 1964) The Microwave Background Radiation (CMBR – Penzias and Wilson 1964) The Big Bang Nucleosynthesis (BBN, 1946) The Big Bang Nucleosynthesis (BBN, 1946) All bear a signature of dark matter All bear a signature of dark matter (BBN also gave the first argument for CMBR, but nobody paid any attention)

106
Physics of Masssive Neutrinos Milos 20-24/05/08 Spin Contribution  Axial Current Going from quark to the nucleon level for the isovector component is standard (as in weak interactions): f 1 A (q)  f 1 A = g A f 1 A (q), g A =1.24 Going from quark to the nucleon level for the isovector component is standard (as in weak interactions): f 1 A (q)  f 1 A = g A f 1 A (q), g A =1.24 For the isoscalar this is not trivial. The naïve quark model fails badly (the proton spin crisis) f 0 A (q)  f 0 A = g 0 A f 0 A (q), g 0 A =0.1 For the isoscalar this is not trivial. The naïve quark model fails badly (the proton spin crisis) f 0 A (q)  f 0 A = g 0 A f 0 A (q), g 0 A =0.1

109
Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS-Directional Rates Good signatures, but the experiments are hard (the DRIFT experiment cannot tell the sense of direction of recoil) Good signatures, but the experiments are hard (the DRIFT experiment cannot tell the sense of direction of recoil) Large asymmetries are predicted Large asymmetries are predicted The rates are suppressed by a factor κ/2π, κ<0.6 The rates are suppressed by a factor κ/2π, κ<0.6 For a given LSP velocity distribution, κ depends on the direction of observation For a given LSP velocity distribution, κ depends on the direction of observation In the most favored direction κ is approximately 0.6 In the most favored direction κ is approximately 0.6 In the plane perpendicular to the sun’s velocity κ is approximately equal to 0.2 In the plane perpendicular to the sun’s velocity κ is approximately equal to 0.2

110
Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS- Modulation in Directional Experiments The Directional rates also exhibit modulation The Directional rates also exhibit modulation In the most favored direction of observation, opposite to the sun’s motion, the modulation is now twice as large. (Maximum in June, Minimum in December) In the most favored direction of observation, opposite to the sun’s motion, the modulation is now twice as large. (Maximum in June, Minimum in December) In the plane perpendicular to the sun’s motion the modulation is much larger. The difference between the maximum and the minimum can be as high as 50%. It also shows a direction characteristic pattern (for observation directions on the galactic plane the maximum may occur in September or March, while normal behavior for directions perpendicular to the galaxy) In the plane perpendicular to the sun’s motion the modulation is much larger. The difference between the maximum and the minimum can be as high as 50%. It also shows a direction characteristic pattern (for observation directions on the galactic plane the maximum may occur in September or March, while normal behavior for directions perpendicular to the galaxy)

117
Physics of Masssive Neutrinos Milos 20-24/05/08 The constrained (σ p,χ,σ n,χ ) plane for the Α=127 system (arbitrary units). Under the curve on the left, if the amplitudes have the same sign and between the curves on the right for opposite sign.

119
Physics of Masssive Neutrinos Milos 20-24/05/08 The directional event rate The event rate in directional experiments is: The event rate in directional experiments is: R dir =(κ/2π)R 0 [1+cos(α-α m π)] R dir =(κ/2π)R 0 [1+cos(α-α m π)] R 0 is the average usual (non-dir) rate R 0 is the average usual (non-dir) rate α the phase of the Earth (as usual) α the phase of the Earth (as usual) α m is the shift in the phase of the Earth (it depends on μ r and the direction of observation) α m is the shift in the phase of the Earth (it depends on μ r and the direction of observation) κ/2π is the reduction factor (it depends on μ r and the direction of observation) κ/2π is the reduction factor (it depends on μ r and the direction of observation) κ and α m depend only slightly on SUSY κ and α m depend only slightly on SUSY